arXiv:astro-ph/0210189v1 8 Oct 2002 † pulsa- ⋆ radial fundamental pul- amplitude Its Galaxy. largest the the terms in kinematic known in sator is III) B2 to The INTRODUCTION 1 o.Nt .Ato.Soc. Astron. R. Not. Mon. cetd....Rcie . . . Received . . . . Accepted h topeeo WVulpeculae in BW Shocks of Pulsationally-Induced Atmosphere the the of Response Spectral c 2 1 yo .Smith A. Myron E-mail:csj@star.arm.ac.uk E-mail:[email protected] rahOsraoy olg il rahB6 D,N Irela N. 9DG, BT61 Armagh Hill, College Observatory, Armagh optrSine oprto/Tc,30 a atnDriv Martin San 3700 Corporation/STScI, Sciences Computer 02RAS 2002 β ehivral WVl(R80,H 910 1V B1 199140; HD 8007, (HR Vul BW variable Cephei 000 1 ⋆ –2(02 rne oebr21 M L (MN 2018 November 4 Printed (2002) 1–12 , n .SmnJeffery Simon C. and xrce rmtefrU otnu,H II He continuum, far-UV the from extracted fipratrdlnsi h pcrm hs ie nld eI He include lines These sho atmospheric spectrum. of the effects in the evaluate lines to about red order over important star in this of days) for 0.201 st data = the echelle before (P of just nights shock three feat second r obtained a shock have shock creates the from it visible where atmosphere forms the photosphere b separated in and phases energetically two envelope upwards at profiles propelled outer line spectral its and flux in continuum grows instability This itso h Idulta h w hc hsslasu osugge o emerges to it infall, us as character from photosphere. leads isothermal layers upper an phases atmospheric on takes upper shock which shock, the two whethewave gradient, of the heating temperature at decreas preferentially atmospheric doublet well-known the ab the II flattens layer C and heating thin the discovery optically of This an of infall. widths win formation the blue short-lived by the a compressed of and development heating the to in due differences that suggests activity uha o h e eIlns nadto,a paetlgi h equiv subtle the by in suggested ca as lag be shock, instead apparent could rebound an levels a addition, atomic photospheric by In excited followed less lines. cooling, from I shock He arising desaturatio lines red of of the degrees curve varying for f from as line so arising by of such indicators attributed regions lags false different Phase be at effect’). may arriving Hoof “Van delay a shock (i.e., a photosphere for evidence no find omto hc waves. shock – formation words: Key bandi 94 ehv netgtdteeuvln itsadsha of and widths evidence equivalent for the investigated lines have We 1994. in obtained S III (Si II C ABSTRACT oprsno eI He of comparison A xetfreiec fwn ntefrbu ig fteU resonance UV the of wings blue far the in wind of evidence for Except WVli eakbefrectn neteeysrn ailpulsatio radial strong extremely an exciting for remarkable is Vul BW λλ λ 588 obe,adohrmdrt eg,S II Si (e.g., moderate other and doublet, 6578-83 77 ie.W aeaddt hs aa3 rhvlIESPeche IUE/SWP archival 37 data these to added have We lines. 5737) λ 60adU otnu u curves. flux continuum UV and 1640 tr:vral:ohr–sas niiul WVl–ln rfie line – profiles line – Vul BW individual: stars: – other variable: stars: ne alia inter ,Blioe D21218 MD Baltimore, e, λ nd 2 85and 5875 † uigteplaincce h pia iepolsremain profiles line shocks. optical supersonic the cycle, highly pulsation as the photosphere During the waves into These waves. emerge wel pulsation as asso propagating upward curve processes with nonlinear velocity ated highly radial from the result features in followi These so standstill immediately “standstill” longer is and, a curve discontinuous 1995) light this, star’s produce Aerts the to in 1981, features as Watson excited & strongly (Stamford mode tion asadhv oprdorrslst the to results our compared have and lags λ 68ln rfie uigtepa fteinfall the of peak the during profiles line 6678 A T λ E tl l v2.2) file style X 60 n eea eoac lines. resonance several and 1640, λ 31 n ihexcitation high and 6371) r ftenx yl.We cycle. next the of art ti h nalshock infall the is it r notemr tenuous more the into . yls Material cycles. 0.8 y efre observers former me v usto cycles pulsation five fmlil lines, multiple of n trst h lower the to eturns λ tti ieare time this at g 85and 5875 e fteoptical the of pes h pulsational the r k nanumber a on cks aitosi the in variations si equivalent in es raino the of ormation v h region the ove tta shock that st sdb post- by used ln width alent rsi the in ures IUE l spectra lle ie,we lines, mode. n λ fluxes 6678, ng ci- l. 2 M. A. Smith and C. S. Jeffery in absorption but undergo extreme variations in shape and (several percent of a stellar radius) as well as its virtual free velocity. Equivalent width variations are also noticeable at fall from maximum to minimum radius. certain phases. In the often-used convention that φ = 0 oc- In the most recent kinematical description, Mathias et curs at light maximum (minimum radius), the radial velocity al. (1998) and Garnier et al. (2002) have summarized the standstill becomes centered at φ = 0.98-1.00. Line profiles present consensus that there are two shocks per cycle. The exhibit double lobes at phases just before (centered at φ ≈ first, “pulsation,” shock is the result of the evolution of the 0.90), and during some cycles just after (φ ≈ 0.06) the veloc- upward-propagating wave which grows in amplitude from ity standstill phase (e.g., Mathias et al. 1998). Adding to the the envelope where it is excited. As it emerges into the at- complexity of description, the radial velocity curve is some- mosphere at φ = 0.1, this shock has a moderately high Mach what sensitive to the method of measurement, the spectral (5-7) number, as referenced by the velocity “discontinuity” and temporal resolution of the observation, and especially just prior to the velocity standstill. A subsequent, “infall,” to the momentary pulsational amplitude of the star, for the shock, occurring 0.8 cycles after the first, is due to the ex- amplitude of the pulsations fluctuate by several percent from treme compression of the upper atmospheric strata as they night to night (Crowe & Gillet 1989, Aerts et al. 1995, Math- fall back and catch up to the slower moving layers of the ias et al. 1998, Garnier et al. 2002). The equivalent widths of lower photosphere. In this picture the line profiles exhibit some metal lines vary with phases as a function of excitation double lobes during the main (and often infall) shock be- potential (Furenlid et al. 1987). The finite signal-to-noise cause of the velocity jump associated with it. Mathias et ratio and temporal sampling frequency of the International al. also note that because the density of the atmosphere de- Ultraviolet Explorer (IUE) observations set practical limits creases monotonically outwards, the infalling region cannot on the otherwise considerable complementary UV informa- be described as a disconnected shell. In addition, Mathias et tion that they offer to optical spectra. al. suggested that shock progresses inward in terms of ab- Despite these observational limitations, important ef- solute (Eulerian; radius from star center) coordinates even fects of the star’s pulsation cycle are readily visible on the as it moves outwards in mass. Thus, their description recon- atmosphere. One of these is a variation of the effective sur- ciles the idea expressed by several previous authors that two face gravity and especially the instantaneous “effective tem- outward-moving shocks per cycle propagate up through the perature” of the star during the cycle. Recently, Stickland atmosphere. In the past the infall shock, which forms at φ ≈ & Lloyd (2002) have compared flux variations at a range of 0.90, has been mistaken for a reflection of a shock from the wavelengths from the far-UV to the near-UV to show that previous cycle off an interior density gradient discontinuity. the effective temperature varies from 20,000 K to 25,000 K In this study we adopt the view of Mathias et al. that this during the cycle. Temperature variations this large may well shock is a natural consequence of infall, and that any ear- cause observable modulations in the mass loss and X-ray lu- lier reflected shock is likely to be damped within the star, minosity (cf. Cohen 2000) of the cycle. rendering it invisible at the surface. Historically, controversy has surrounded the interpreta- The elusiveness of even a qualitative interpretation of tions of the profile and strength variations caused by shock the shocks in BW Vul has slowed the necessary develop- waves moving through the atmosphere of BW Vul. One of ment of self-consistent radiative hydrodynamical models. these is the so-called “Van Hoof effect,” named after its pri- Early on, Stamford & Watson (1978) assumed that a large- mary discoverer (Van Hoof & Struve 1953). This effect is the amplitude velocity piston at the base of the atmosphere purported phase lag between the velocity curves extracted developed into a thin, isothermal shock as it progressed from lines formed at different atmospheric depths. This is through the line formation region. Using this dynamical thought to be the result of the finite travel time required for model atmosphere, they constructed line profiles of Si III a pulsational shock wave to move up from one region of line λ4552 at several key phases in the cycle. Profiles at phases formation to another. In the most recent such report, Math- we now call the infall shock exhibited line doubling (albeit ias et al. (1998) reported that double line profiles of various over only a brief interval). In subsequent work Stamford & lines observed near φ ≈ 0.9 and sometimes 0.1 can exhibit Watson (1981) placed a large, adiabatic sinusoidal velocity equal blue-red strengths at slightly different phases. A re- variation at the base of a gray model atmosphere and demon- lated issue is the cause of the line doubling itself. Odgers strated that an isothermal shock developed in the line forma- (1955) and Goldberg, Walker, & Odgers (1976) first at- tion region. Although they did not compute line profiles in tributed the velocity discontinuities to atmospheric absorp- these simulations, Stamford & Watson stated that they an- tions just below and above the shock. These authors argued ticipated that the shock would produce line doubling during that as an upward-propagating pulsation wave breaks into the shock passage. The 1978 Stamford & Watson paper to a shock it accelerates the line forming regions of the atmo- date represents the only attempt to compute the line transfer sphere from the lower photosphere, thereby creating a den- for a spectral line in a moving model atmosphere appropriate sity discontinuity with respect to the lower photosphere. The to BW Vul. Recently, Owocki & Cranmer (2002) have devel- semi-ejected “shell” coasts to some maximum height and re- oped hydrodynamic models that roughly simulate the ve- turns ballistically to these lower strata. In contrast, Young, locity and light variations of the pulsating star. Their mod- Furenlid, & Snowden (1981; YFS) suggested that turbulence els assume strong outgoing shocks in realistic atmospheres. and pressure effects are the chief causes of the profile dou- The shocks begin in the envelope as a large-amplitude pul- blings at these phases. In their picture the standstills are sation wave, break into a small-amplitude shock in the lower caused by line formation in both a lower stationary atmo- photosphere, and evolve into an isothermal, large-amplitude spheric region as well as an infalling zone rendered trans- (60× in density) shock in the wind. Owocki & Cranmer’s parent by its lower density. All these studies have pointed results show that the shock has the effect of flattening the to the extended displacements of the line formation region atmospheric density gradient well out into the wind, thereby

c 2002 RAS, MNRAS 000, 1–12 Shocks in the Atmosphere of BWVul 3 explaining the large range in phase over which the shock can Table 1. Journal of Year 2000 Observations (HJD - 2400000) be traced in the UV resonance lines. As these waves emerge into the wind, they can impact slower flows, causing reverse shocks and the formation of Discrete Absorption Compo- Night 1 (Sept. 17/18) Night 2 (Sept 18/19) Night 3 (Sept. 19/20) nents (DACs) in the far blue wings, indeed as observed in 51805.574 51806.560 51807.568 the Si IV and C IV lines (Burger et al. 1981, Blomme & 51805.579 51806.564 51807.578 Hensberge 1985, Massa 1994). 51805.583 51806.569 51807.585 The idea of a strong shock front moving through the 51805.588 51806.574 51807.593 atmosphere is of course not limited to β Cephei variables. 51805.593 51806.579 51807.599 In fact, the concept of a vertically propagating “hot front” 51805.597 51806.584 51807.604 was first used by Merrill (1955), referring to line doubling in 51805.602 51806.589 51807.609 both absorption and emission lines in long period variable 51805.607 51806.593 51807.613 stars. While this still represents the common interpretation 51805.612 51806.600 51807.617 of this spectroscopic phenomenon in the LPV stars (e.g., Al- 51805.616 51806.606 51807.621 varez et al. 2000), the idea of shocks heating the atmosphere 51805.621 51806.612 51807.651 51805.625 51806.620 51807.655 have not taken root in most discussions of the dynamics of 51805.629 51806.626 51807.659 the BW Vul atmosphere. This is perhaps because emission 51805.633 51806.632 51807.754 components have not been observed in BW Vul’s spectrum. 51805.637 51806.638 51807.759 In fact, the only evidence given for shock dissipation and 51805.643 51806.646 51807.764 heating appeared rather recently, in Furenlid et al.’s (1987) 51805.649 51806.653 51807.767 discussion of variable O II lines. The subject has been virtu- 51805.653 51806.657 51807.771 ally ignored since, and we will revive this discussion in this 51805.657 51806.662 51807.775 paper. 51805.661 51806.666 51807.781 The present paper was motivated partially by our im- 51805.665 51806.671 51807.785 pression that an understanding of the shock wave proper- 51805.672 51806.677 51807.789 51805.676 51806.681 51807.793 ties has been hampered by uncertainties in spectroscopic 51805.680 51806.686 51807.797 measurements and interpretation. For example, YFS and 51805.684 51806.691 51807.801 Crowe & Gillet (1989) found widely different average equiv- 51805.688 51806.696 51807.805 alent widths for the important C II λλ6578-82 lines. Yet the 51805.692 51806.701 51807.809 “large” values found by YFS during the distension phases 51805.696 51806.705 51807.813 formed the basis of their conclusion that line doubling and 51805.700 51806.710 51807.817 strengthening is caused by changes in atmospheric contin- 51805.704 51806.715 51807.821 uous opacity. This suggestion though oft-quoted has gone 51805.708 51806.720 51807.826 untested. We also realized in planning our program that the 51805.715 51806.724 51807.830 existence of a Van Hoof effect could be tested by compar- 51805.719 51806.728 51807.834 51805.723 51806.732 51807.838 ing the responses of the red He I λ5875 (triplet) and λ6678 51805.727 51806.736 51807.843 (singlet) lines, which probe slightly different column lengths 51805.731 51806.740 51807.849 through their gf difference, and also volume densities be- 51805.735 51806.747 51807.855 cause of the triplet line’s mild sensitivity to density through 51805.739 51806.751 51807.860 the partial metastability of its lower level. These lines have 51805.743 51806.755 51807.865 heretofore not been monitored in BW Vul. Other significant 51805.747 51806.759 51807.871 but so far unremarked lines in the red region are the Si II 51805.751 51806.764 51807.876 λ6371 and Si III λ5737 features, which together provide a 51805.759 51806.770 51807.882 measure of variations in the atmosphere’s ionization equi- 51805.763 51806.774 51807.887 librium. The echelle data we have obtained sample forma- 51805.768 51806.778 51807.893 51805.772 51806.782 51807.898 tion conditions of many lines at the same time and thus 51805.776 51806.787 51807.904 can provide accurate phasing information from this variable- 51805.781 51806.791 51807.909 amplitude pulsator. This simultaneity permits us to remove 51805.785 51806.795 51807.916 past ambiguities in correlating behaviors of various lines at 51805.789 51806.798 - different epochs. A second reason for undertaking this study 51805.793 51806.803 - is the availability of largely unanalyzed IUE data from sev- 51805.800 51806.808 - eral cycles at nearly the same epoch. This dataset permits us 51805.810 51806.813 - to tie together the resonance lines and high-excitation opti- 51805.815 51806.818 - cal lines formed deeper in the atmosphere at a large number 51805.819 51806.822 - of phase reference points in the pulsation cycle. 51805.823 51806.827 - 51805.832 51806.832 - 51805.837 51806.837 - 51805.841 51806.842 - 2 OBSERVATIONS 51805.846 51806.847 - 51805.851 51806.851 - 2.1 Observations and reduction details - 51806.856 - The optical data for this study were obtained on the nights of 2000 September 19–21 with the Sandiford echelle spectro-

c 2002 RAS, MNRAS 000, 1–12 4 M. A. Smith and C. S. Jeffery

Table 2. Summary of Atomic Data for Lines in McDonald Spec- made. Rectification of echelle orders was performed by an tra interactive polynomial fitting procedure. Orders were then spliced at wavelengths for which flux contributions of ad- joining orders were equal. We measured the radial veloci- Wavelength Ion χ (eV) log gf ties of strong lines by cross-correlating the lines against a 5606.09 S II 13.8 0.16 reference line profile observed near φ=0.2. Profiles at this 5639.980 S II 14.1 0.33 phase are approximately symmetric and exhibit an approxi- 5640.314 S II 13.8 0.15 mately mean width and thus lend themselves to comparison 5646.979 S II 14.1 0.11 with profiles of extrema phases. We determined true equiv- 5648.070 C II 20.8 -0.45 alent widths of these lines and other analyzed features in 5639.980 S II 14.1 0.33 the McDonald spectra by an interactive computer algorithm 5640.314 S II 13.8 0.15 tailored for this application. The program uses input wave- 5659.956 S II 13.7 -0.07 5662.460 C II 20.8 -0.27 length ranges over which both the continuum and the line’s 5666.629 N II 18.5 0.01 absorption profile are to be extracted. The continuum level 5676.017 N II 18.5 -0.34 is then fixed by a specified “Nth percentile brightest flux” 5679.558 N II 18.6 0.28 among candidate fluxes in the continuum window. The value 5686.213 N II 18.6 -0.47 of N, typically ≈80%, can depend on the presence of nonstel- 5696.603 Al III 15.7 0.23 lar features but is well suited to modification interactively 5710.766 N II 18.6 -0.47 when such unwanted features appear as telluric lines, cosmic 5722.730 Al III 15.7 -0.07 rays, or fringing. 5739.734 Si III 19.8 -0.160 5747.300 N II 18.6 -1.020 5833.938 Fe III 18.6 0.616 2.2 IUE Spectra 5875.615 He I 21.0 0.41 6247.178 Al II 16.6 -0.20 In order to avoid uncertainties in the absolute calibration 6346.859 N II 23.3 -0.86 of fluxes, we made use of 38 high-dispersion echellograms 6371.371 Si II 8.2 0.00 obtained with the SWP camera through the large aper- 6379.617 N II 18.5 -0.92 ture during monitoring campaigns on the star in October 6562.801 H I 10.20 -0.69 and November 1994. “NEWSIPS” extractions were down- 6578.052 C II 14.5 0.12 1 6582.882 C II 14.5 -0.18 loaded from the MAST web-based archives. Absorption line 6678.154 He I 21.3 0.33 strength indices (LSI) were then calculated by ratioing the total net (uncorrected for ripple distortion) flux in a nar- row band centered at line center to the total net flux in the parent echelle order. Such indices are not true equivalent graph (McCarthy et al. 1993) attached by fiber optics to the widths, but they are directly proportional to them and in- cassegrain focus of the Struve 2.1-m telescope at McDonald crease with absorption strength. Because these indices are Observatory. The cross-dispersing prism in this instrument insensitive to continuum placement, and (as defined herein) was rotated to select a central wavelength of 6120A˚ and to independent of errors in blaze function (“ripple”) correction, include a nearly continuous wavelength range (22 orders) of they are unambiguous measures of the absorption for pre- λλ5510-6735 on a 1200 × 400 CCD detector. This configu- scribed velocity limits, and they are particularly accurate ration resulted in a spectral resolution of 45 000 and a pixel differential measures of line strength differences for an IUE −1 −1 spacing of 2.8 km s pix . Signal-to-noise ratios of 200– time series. The line fluxes were measured between velocity 300 were typically attained in integration times of 5–6 min- limits of generally ±1.0 A˚ of line center, where the radial utes, except at high airmass when they were increased to 7–8 velocity of the star was referenced at –10 km s−1. Because minutes. (The profiles displayed in Fig. 7 of this paper were the radial velocity of the star changes dramatically through exposed 5–6 minutes.) Flat and comparison lamp spectra the cycle, we first determined spectrum-to-spectrum shifts taken at various times of the night showed that the contin- in pixel space before co-adding spectra in a co-moving frame. uum and wavelength stability of the spectrum was robust. A table of the mid-observation times for the three nights is compiled in Table 1, while a line list of identified features in 2.3 Radial Velocity Ephemeris our spectra is given in Table 2. The wavelengths and exci- Although there is unanimity that BW Vul is monoperiodic tation potentials listed are obtained from the Kurucz line (with P ≈ 0.201043), some controversy has surrounded the library (Kurucz 1990). “drifting” of its pulsation period derived from datasets of The spectra were kindly reduced (background- different epochs. Various authors have suggested ephemeris subtracted, extracted, and flatfielded) by Dr. Chris Johns- corrections for a quasi-evolutionary lengthening, light travel Krull using computer codes described by Hinkle et al. (2000) time across a binary, and both random and discontinuous and Piskunov & Valenti (2002). Wavelengths were deter- changes for unspecified reasons. In past years support has mined by an interactive graphics package that allowed a built for the binarity solution with an orbital period near solution simultaneously in the echelle and cross-dispersion 34 years (Pigulski et al. 1993, Odell 1994, Horvath, Gherega axes (Valenti, priv. comm.). Solutions were obtained by min- imizing residuals between laboratory and observed Th and Ar line wavelengths and iteratively rejecting outliers. Cor- 1 Multi-Mission Archive at Space Telescope Science Institute, rections for terrestrial orbital and rotational velocities were under contract to NASA.

c 2002 RAS, MNRAS 000, 1–12 Shocks in the Atmosphere of BWVul 5

the cycles on the three nights of our observations. We de- termined an instrumental systemic velocity of the star by comparing the centroid wavelength of symmetric line pro- files with nearby Th-Ar features in our emission spectra and correcting them for the Earth’s orbital and rotational veloci- ties. We then averaged all the velocities around their respec- tive cycles. The resulting mean heliocentric radial velocities found for BW Vul from the three nights were –7.7, –10.3, − − and –11.4 km s 1. The resulting mean of –9.7 km s 1 is in excellent agreement the mean value of –9.2 km s−1 given by Mathias et al. In Figure 1 the radial velocities are shown for the HeI λ5875 for all the three nights. It was possible to measure the equivalent widths of the lines arising from highly excited atomic levels, but these often were both weak- ened and broadened to invisibility during the critical shock passage phases. Radial velocities are also given in Fig. 1

−1 for SiIII λ5740 and Si II λ6371 (the latter can reliably be Figure 1. Radial velocity in km s determined from cross- measured only in the phase ranges 0.1 <φ< 0.85). The correlations on the He I λ6678 (pluses), Si III λ5740 (crosses) and silicon lines have velocity amplitudes 5-10% larger than the Si II λ6371 (asterisks) lines of BW Vul for all three nights of this study, 2000 September 19-21. Note that the He I velocities have helium line curves and even more striking discontinuities at been rescaled by factors of 1.10, 1.05, 1.05 to match the Si II line the beginning at end of standstill. The Hα velocity curve velocity amplitudes. The squares at the top of each panel denote (not shown) has even a slightly smaller amplitude and less the reciprocal (with offsets of ∼+100) Si II equivalent widths; steep “discontinuities” than the He I line curves do. We be- these could not be measured for phases near zero when the two lieve that these are effects of the far wings of the helium and shocks occur. hydrogen lines, which tend to broaden the cross-correlation function and produce artificially small velocity differences for the line core. Aside from this anomaly, the silicon line & Farka 1998), although it appears possible that small ran- velocities are similar to the helium ones. All these transi- dom changes can also alter the phase zeropoints from time to tions have moderate to high excitation potentials (>20 eV) time (Sterken 1993). We have adopted the binary + secular- and are saturated. Thus, in static atmospheres without the lengthening solution of Horvath et al. for the light minimum imposition of shocks one expects them to be formed in the phases. Light minimum is the recommended new benchmark lower photosphere close to the continuum formation region. because it can be determined with greater precision (Sterken Thus it should not be surprising that they do not show phase 1993). To these calculated phases, we have added 0.48 cy- lags (Van Hoof effects). By comparison, we also exhibit in cles (Furenlid et al. 1987, Stickland & Lloyd 2002) to refer- the upper region of the three panels of Figure 1 the equiv- ence them to the traditional zero at optical light-maximum. alent widths of the Si II λ6371 line over those phases out- This is also the approximate midpoint of the radial veloc- side the shock intervals - these are the times when the line ity standstill. This ephemeris agrees to within 0.015 (±0.02) was strong enough that reliable centroid positions could be cycles of the midpoint occurrence of the standstill in our measured. On Nights 2 and 3 one sees that the phases of McDonald data. The relative phases of the 1995 IUE epoch velocity maximum extend slightly longer in the Si II feature did not match as well, giving a difference of 0.09 cycles from than in the He I line, causing a slight delay in the onset of this ephemeris relative to the standstill occurrence found by the standstill for the He I line curves. We believe that this Stickland & Lloyd. We have referred our φ = 0 fiducial to the is an artifact of a relatively “late” desaturation of the blue Stickland & Lloyd phase φ = 0.10, which takes into account lobe of the weaker Si II line, causing the line’s centroid ve- that the latter authors tied their zeropoint to radial velocity 2 locities to remain at negative velocities for a longer time maximum instead of the usual velocity standstill criterion. and to later phase than the other lines measured (see §4.4). We note also that the average radial velocity of the two red He I lines during standstills of each of the three nights was −1 3 RESULTS –8.3, +2.8, and –11.6 km s , respectively, giving a mean of –6 km s−1. This is very nearly the systemic velocity of 3.1 Radial velocities the star, a result similar to that found by Mathias et al. (1998). Finally, differences among the two He I lines and the A large number of radial velocity curves have been discussed −1 Si II line averaged ±4 km s , so it is likely that there are for BW Vul from as many optical datasets. We decided to minor cycle-to-cycle differences in the mean velocity of the focus our work on the radial velocities of the red helium standstill. lines and primarily for the purposes of checking the phase zeropoint and to search for differences in amplitude among Figure 1 provides a useful means of correlating the He I line velocities with equivalent width changes for this and other lines during the cycle. Notice first the clearly de- 2 Note that the photometric standstill occurs just before the on- fined standstill of the velocity curve, lasting some 0.16 cy- set of velocity standstill and is much shorter. These respective cles. This feature can be used to check the phase zeropoint standstills last about 0.03 and 0.15 cycles (see e.g., Furenlid et al. given in past ephemerides. The features of the standstill are 1987). found to be similar in form, whether determined from a line-

c 2002 RAS, MNRAS 000, 1–12 6 M. A. Smith and C. S. Jeffery

Figure 2. Equivalent widths of He I λ6678 with phase for the Figure 3. C II λ6578, λ6583 equivalent width curves for the three nights of study; offsets of -0.3A˚ and -0.6A˚ are introduced three nights in this study. The values for λ6583 are scaled by for visual clarity. Approximate error bars are indicated. factors of 1.3, 1.1, and 1.2 for the three nights, respectively, to match the λ6578 data. centroiding technique or from fitting two gaussians when they appear. Additionally, the feature also shows a shallow positive slope, as several other investigators have noted who 3.2.2 The CII λ6578, λ6583 doublet and high-excitation used a different (double-gaussian) velocity measurement cri- lines terion. The standstill velocities are near zero or slightly neg- The CII λ6578, λ6583 doublet is located close to the Hα ative. In addition, Fig.1 indicates that the positive velocity line and arises from a similarly excited level of 14.4 eV. It amplitudes, and phases of the quasi-discontinuity leading to has thus long served as a conveniently accessible tempera- the standstill, can change from one cycle to the next. We can ture probe for atmospheres of variable B stars. We measured speculate that these differences reflect the variable pulsation the true equivalent widths of each of these lines in the same shock strengths from the preceding cycles. manner as the He I lines. These are exhibited in Figure 3, where we have represented the two lines by different symbols and rescaled the equivalent widths of λ6583 to the slightly larger ones of λ6578. Some of the scatter at like phases arises 3.2 Behavior of the Excited Optical Lines from measurements at adjacent pulsation cycles. The gf ra- tio of the components is 2. The observed ratios do not show 3.2.1 The red He I lines evidence of variations during the cycle, and their nightly The accurate measurement of equivalent widths of lines in means, 1.28, 1.14, and 1.16, show clearly that even though the BW Vul spectrum is challenging because the positions, the lines are comparatively weak they are quite optically widths, and core depths vary dramatically over the cycle. We thick. began our study by investigating equivalent widths for the Our C II doublet curves in Fig. 3 exhibit well defined λ5875 and λ6678 lines. These He I transitions are, respec- minima that coincide in phase with the broad minimum tively, analog triplet and singlet 2P-3D transitions, and each found by Crowe and Gillet (1989), except that the latter has excitation potentials of 21 eV. Although variations of the authors’ data do not hint at a separation in phase between neutral helium line have not yet been studied in this star, the two individual shocks. The C II curves are also very sim- their importance cannot be overstated because of the lines’ ilar to those shown for the residual intensity of the Hα core sensitivity to atmospheric heating. Furenlid et al. (1987) re- discussed by Crowe & Gillet (1989). We have confirmed this ported unambiguous evidence for a temperature rise from behavior for the core of this line in our data and have also increases in the ratio of a pair of O II and Fe III lines during found that the equivalent widths extracted from small wave- the velocity-standstill phase. Figure 2 shows the variation of length windows centered on the core exhibit a similar be- the true equivalent widths for the He I λ5875 and He I λ6678 havior. The effect rapidly disappears and even inverts as lines for all three nights. These plots exhibit generally two one includes more and more contribution of the Hα wings maxima, the stronger of the two centered at the occurrence in the window. These results confirm that the variations are of the infall shock at φ≈ 0.90-0.95. The equivalent width ra- produced by localized atmospheric strata. Other moderate tio of these lines is 1.13±0.03 outside the “windows” of the to high excitation lines such as N II λ5710 (χ = 18.5 eV) two shock intervals. Because the ratio of their atomic gf’s is and SII λ5640 (13.8 eV) produce variations similar to the two, the observed ratio indicates that the features are very C II doublet, but the intrashock maxima for them are not optically thick. The measured ratio is almost the same dur- always so clearly separated in phase. For phases outside the ing the passage of the pulsation shock, but it increases to a two shock intervals, many of the lines in our sample broaden mean value of 1.23±0.08 during the infall shock. and fade to below our detection threshold.

c 2002 RAS, MNRAS 000, 1–12 Shocks in the Atmosphere of BWVul 7

3.2.3 Si II λ6371 and Si III λ5740 lines The SiII λ6371 and Si III λ5740 lines are important because they arise from atomic levels having the largest combined excitation and ionization potentials of all the lines in our optical coverage, save the He I lines. In addition, their com- bined responses furnish information on changes in the ion- ization equilibrium in this atmosphere during the pulsation cycle. In investigating the strengths of these lines, we found first that the SiIII λ5740 line shows only mild increases of ∼10–50% in equivalent width from night to night during shock passage. This is because the ionization equilibrium of silicon is roughly balanced between Si+1 and Si+2. How- ever, as the dashed lines at the top of each of the panels in Figure 1 show (plotted are the reciprocals of the line Figure 4. UV continuum fluxes at ∼λ1850 (diamonds) and line strength), the response of the Si II λ6371 line can be quite strength index for He II λ1640 (crosses). The latter, denoted LSI, pronounced. During the passage of the second (pulsation) is defined in §2.2. UVC fluxes are plotted relative to the mean, but shock, the λ6371 broadens and weakens so much that its 0.7 units are subtracted from the He II LSI to separate the curves. velocity centroid cannot be reliably measured. As indicated Symbols for data above φ = 1.0 are repeated and rendered small. in Fig. 1, the phases of maximum weakening do not coincide The dashed line through the He II curve is a reference sinusoid: solid line is a compressed/stretched curve around the sinusoid (see with the shock passage but rather are delayed by 0.10 cycles text). Note the slight bump in the He II curve for data in the φ after the end of the standstill phase, when the strengths of range 0.2–0.28 and the weak dip at 0.15–0.2. Approximate error the excited lines are slowly decreasing. bars are shown. Figure 3 gives an indication of the variations in shock heating and of the inequality of heating amplitudes between the two shocks. One can see this, first, in the amplitude be an underresolved rendition of two peaks apparent in the variations in the shocks (as judged by the sharpnesses and line strength curves at φ = 0.9 and 0.1. This double-peaked depths of the C II minima) and, second, in the variation of structure is completely unresolved in optical light curves (cf. the strengths of the Si II line and other moderate excita- Fig. 3 of Stickland & Lloyd 2002). Note also that the scatter tion lines, e.g., S II λ5640. These diagnostics generally im- is small and does not seem to reflect the obvious cycle-to- ply that the temperature increase associated with the pulsa- cycle differences at some phases in the radial velocity curves. tional wave is the stronger of the two shocks. This is contrary The HeII λ1640 absorption curve is morphologically very to the inequality of the shock jumps (Fig. 1; see also Mathias similar to the UVC curve. The curves extracted from the et al. 1998). We also note for discussion below that the phase blue and red halves of the profile are in turn identical to one of equivalent width minimum is delayed by 0.07–0.08, both another. The similarity between the UVC and He II curves is with respect to the line’s radial velocity minimum (Fig. 1) the result of the proximity of the depths of formation of this and with reference to the C II equivalent width minimum at line and the continuum. However, the slight tendency of the φ = 0.1. HeII curve to flatten at the maximum- and minimum-flux phases is likely caused by both the core and line (formed over different depth ranges) being sampled in our extraction. A 3.3 Ultraviolet lines slight bump in the He II curve at φ ≈ 0.20–0.28 is visible in Except for the He II 1640A line (“helium Hα,” χexc = 41 Figure 4 and is also reproduced in the UVC curve. To clarify eV), the UV lines used in this analysis are all resonance lines. this bump and the weak dip occurring at a phase just before To varying degrees the latter lines have components formed it (φ = 0.15–0.20), we overplot two curves in Fig. 4. The first both in the static line forming region (upper photosphere) is a simple sine curve (dashed line), and the second (solid and the accelerating wind. We will treat these lines in order line) is a sine curve that has been compressed/stretched in of likely formation depth, starting from the He II feature, the first and second quadrants. No matter how one chooses and work our way up through ionization potential out into a fitted curve to the observed values (from three different the wind. pulsation cycles) the dip and bump features fall outside the error limits. These weak features are also visible in the two UVC curves of Stickland & Lloyd, based on 21 additional 3.3.1 HeII λ1640 spectra and from data processed and extracted by different algorithms from ours. These are undoubtedly real, and we Figure 4 depicts the extracted UV continuum (UVC; rep- comment further on them in §4.1. resenting λλ1800-1905) light curves from the 37 available large-aperture IUE/SWP spectra obtained in 1994, together with the extracted line strength index created from ratios of 3.3.2 Resonance lines of moderately excited ions: Al III, fluxes within about ±1.6 A˚ of He II line center to all the SiIII, and SiIV other net (ripple uncorrected) fluxes in the echelle order containing the line. The detailed shape of the UVC curve Figure 5 depicts the UVC and absorption curves for the lines is in excellent agreement with the two plots constructed by AlIII λ1855, Si III λ1206 and Si IV λ1394. We have inverted Stickland & Lloyd (2002) from essentially the same data. the Al III and Si III curve in these plots to facilitate a com- The curve shows a broad, asymmetric maximum which may parison among all four curves. Curves extracted from the

c 2002 RAS, MNRAS 000, 1–12 8 M. A. Smith and C. S. Jeffery

blue wing (wind absorption) in the measurement, the on- set and extension of the maximum-strength phase shifts to later and later phases. Thus, this appearance of the shock as a long-lived feature in the wind is responsible for the pos- itive phase shift of the “C IV blue” and “N IV blue” curves relative to the “C IV red” plot in this figure.

4 DISCUSSION 4.1 “Phase lags” reinterpreted The combination of optical and UV resonance line results requires a picture which integrates the effects of the pulsa- tion and infall-generated shocks. Figures 4, 5 and 6 record the differences in UV line responses with increasing ioniza- Figure 5. UV continuum fluxes at ∼λ1850 (diamonds) and line tion potential. Massa (1994) has depicted the acceleration of λ λ λ strength indices for the Al III 1855, Si III 1206, and Si IV 1394 C IV, Si IV, and Si III in grayscale IUE 1979 spectra. These resonance lines. The line strengths are obtained from the cen- spectra show that the wind features start 0.1 cycles after tral profile within about ±0.8 A˚ of line center and refer to the strength of the continuum. In the case of Si III and Al III the in- the passage of the pulsation wave through the photosphere. dices is inverted because the line responds oppositely from the The photospheric and wind components of C IV are at times other features. Error bars are indicated. co-mingled, but otherwise there is no hint of a graduated response through the photosphere. Rather, there seem to be separate responses from two discrete “photospheric” and “wind” regions. In particular, continuum fluxes and lines of high excitation, such as HeI, HeII, and SiIII, show no per- ceptible phase differences in their velocity or line strength responses. Even the line strength minima of the moderate excitation C II doublet (χ = 14 eV) seem to coincide with the appearance of the shocks just prior to and following the end of the velocity standstill. These lines collectively span a large range in excitation. Lines arising from less excited lev- els than 14 eV, such as the resonance lines of Al III or moder- ate excitation lines of Si III (Stickland & Lloyd 2002), cannot be measured precisely enough in IUE spectra to search for phase lags with respect to the optical lines. In fact, we find that in order to see any obvious indication of a phase lag after the passage of the excited lines one must search in the far blue wings of the resonance lines. Perhaps this should not be a surprise. According to the Owocki & Cranmer (2002) Figure 6. UVC fluxes (diamonds) and line strength indices for simulations, the UV absorption features form over length Si IV λ1394, C IV λ1548, and N V λ1238, either blue or red por- tions of the profile, as indicated. The windows sampled are about scales much longer than the effective depth of the static line ±0.8A˚ around line center. Error bars are indicated. formation region. Thus, there is ample column length over which shock-induced features can develop. If there are no phase delays among the excited optical blue halves of the Si III and Si IV lines have 10–20% larger lines, what is one to make in Figure 1 of the apparent phase amplitudes than the red halves but otherwise are similar. delay of 0.07–0.08 after the Si II λ6371 curve? We believe Note first that the Si III curve weakens (rises) more quickly the key here is that Si+1 is a trace atmospheric ion, which is than Si IV strengths during the phase interval 0.7–0.9. This therefore sensitive to temperature and not that its mean line is likely to be a consequence of Si+3 being the dominant formation region is so high in the atmosphere that it takes ion in the atmosphere, and Si III responding (decreasing in the shock a finite time to reach it. Consider as a more plausi- strength) more readily to heating that accompanies the in- ble circumstance that the formation regions of most optical fall shock at φ ≈ 0.9. Secondly, note that as one proceeds lines largely overlap. The so-called “delayed” weakenings of from the AlIII through the SiIV curves, the maximum ab- the Si II feature may more easily represent the subsequent sorptions of the excited ions extend over longer and longer passage of a cooler medium. We have in mind the post-shock intervals. Figure 6 demonstrates that their long-lived char- region which is cooler and more tenuous than the shock in- acter continues for the C IV λ1548 and N V λ1238 (blue half terface (Liberman & Velikovich 1986). A strong post-shock only) features. For these lines one sees that this plateau ex- rarefaction is clearly visible in the hydrodynamic simulations tends to φ ∼ 0.4, which is some 0.3 cycles after the shock of Owocki & Cranmer (2002) and indicate a rough “half- passes through the photospheric line formation regions of wavelength” of ∼0.25 cycles. From this result one might an- C IV and N V. Experimentation with extractions along the ticipate the effects of a rebound shock having approximately C IV profile indicates that as one includes more and more this delay. Altogether, we can speculate that the marginally

c 2002 RAS, MNRAS 000, 1–12 Shocks in the Atmosphere of BWVul 9

ening of the blue wing. In these plots we exhibit this fact by multiplying the depth of λ6678 on the blue wing (and also extreme red wing) by a factor of 1.4 to 1.8. Figure 7 shows that blue wings of the λ6678 scaled by these factors indeed replicate the λ5876 absorptions at this phase. We see this phenomenon over a total range of 0.08–0.10 cycles centered on radial velocity maximum (φ≈0.91) on each of the three nights. In these various examples the limiting line- depth scaling factor appears to be about 2.0. Since this is also the gf ratio of the lines, it is likely that these extra ab- sorptions are due to the medium at negative velocities being optically thin to He I line radiation. An alternative possibil- ity, that the excess arises from metastability of λ5875, is implausible because no such excess absorption is present in this line during the distension (low-density) phases at φ ∼ 0.5. If temperature variations cause the changes in the blue Figure 7. Profile for the red λ5876 (dashed) and λ6678 (solid) wings of the He I lines, there should be a similar response in He I lines, which have an atomic gf ratio of 2:1, at a phase near φ the inner blue wing of the C IV doublet members - the cores = 0.90 on each of three nights. Also depicted are the λ6678 feature scaled by a factor of 2 (dotted line), as well as this same feature of the Si IV lines are too broad to demonstrate this. Fig- (thick dot-dashed) scaled by the indicated scale factor given next ure 8 implies that the absorption-scaling argument is likely to the solid dot. This figure suggests that the “excess absorption” to be valid, that is, that an excess absorption at about –100 −1 of the blue segment of both lines is due to optical thinness of the km s of line center is caused by an optically thin column at line at negative velocities. The lines seem to be strictly optically these shifted wavelength. (By “excess,” as for the He I lines thin (ratio of 2) up to about –30 km s−1 on “Night 3” (September in the previous figure, we refer to the absorption in the blue 21). wing of the stronger λ1548 line relative to λ1550.) Massa’s (1994; see Fig. 3) grayscales exhibit this same effect – as a low-velocity “spur” occurring ∼0.1 cycles before the wind acceleration manifests itself at more negative velocities.

4.3 C II line strength variations The reader will recall that Young, Furenlid, & Snow (1981) first drew attention to C II variations during the cycle of BW Vul and posited that the C II variations were the result of the lines growing anomalously strong outside the shock phases. To test this assertion, we have synthesized the C II doublet with the Hubeny SYNSPEC (Hubeny, Lanz & Jef- fery 1994) line synthesis code using Kurucz (static!) model atmospheres. For an atmosphere having Teff = 23000K, −1 log g = 4, and ξt =5 kms , we found an equivalent width of 0.22 A˚ for λ6578 and a λ6578/λ6583 ratio of 1.14. Nearly Figure 8. Montage of C IV profiles (λ1550 overplotted onto λ1548) at φ ≈ 0.9, showing the optical thinness of the low ve- identical results obtain for log g = 3. These values com- locity blue wing at this phase. The observations, SWP 52644-5 & pare well with our mean observed λ6578 equivalent width SWP 52880, were taken in 1994 - the first two on HJD 2449650.2 value of 0.235±0.015 A˚ for phases outside the shocks and and the third on HD 2449679.8. with the corresponding mean observed ratio of 1.19. Our modeling also shows that the strengths of these lines are quite insensitive to changes in temperature in the domain visible bumps in the UVC and He II strength curves at φ ≈ 20 000–25 000 K. The models do not confirm the speculation 0.23 are produced by a small temperature enhancement due by YSF that changes in atmospheric density play a strong to the rebound. In this picture the abrupt-appearing end of role in determining the line strength changes during the cy- the UVC maximum would be the result of particles entering cle. Of course, the line strengths will increase appreciably the cooled post-shock flow. with any microturbulence that might accompany the shocks, so this would not explain the decrease during these phases. The upshot of these calculations is that the decreases in C II 4.2 Blue wing strengthenings (moderate strengths observed at shock phases cannot be due to simple velocities) changes in atmospheric temperature or density. Thus, our To gain some insight into the cause of the equivalent width results suggest that the question to pose is not “why are variations of the red He I lines exhibited in Fig.2, we ex- the C II strengths large during the non-shock phases?,” but amined the shapes of the two lines as a function of phase. rather “why do the C II strengths decrease to smaller values Figure 7 illustrates that the cause of the equivalent width than they should have during shock phases?” The question is maximum of λ5875 at φ = 0.9 on each night is a strength- critical to a discussion of the shocks in BW Vul’s atmosphere

c 2002 RAS, MNRAS 000, 1–12 10 M. A. Smith and C. S. Jeffery

velocities (Furenlid et al. 1987). Strata just below them fall slightly more slowly, and so on, down to the fully-braked sta- R tionary layers. These combined decelerations produce com- pression over a broad range of layers. The result of this pile up is a conversion of differential flow velocity to local heat- ing. Indeed, this effect can be observed as the first maximum of the UVC and He II line strength curves at φ = 0.85–0.1 (i.e., at velocity maximum) and by the disappearance of the cool-gas diagnostic, Si II λ6371, at the same times. Heating
will increase the number of atoms in excited states and thus





should permit new optically thin absorption to appear in the










excited He I lines. This absorption is formed in a still-falling






column which is still high enough in the atmosphere to be




optically thin to an external observer. Most of the initial col-





umn density will be concentrated near the shock, so the lobe

will appear at near-rest velocities. As this pile up proceeds, compressional heating
the threshold column density needed for visibility will re- τ =1


z λ cede (moving upward, in Eulerian coordinates), permitting λ the optically thin absorption in the profile to grow toward F positive velocities until it runs into and merges with the op- λ tically thick red lobe. The process ceases when the deepest φ 0.800.86 0.91 0.96 1.02 layers essentially at rest become optically thick to the ob- server. At this point, just after phase 0.0, the entire profile Figure 9. Schematic illustration of the formation of the He I becomes optically thick over a broad distribution of line ve- λ5876 line profile as it evolves through radius minimum. The top panel suggests the overall behaviour of the stellar radius. The locities, both from the still-falling column and the strata at five bottom panels approximate the apparent line profile (F (λ)) rest at the bottom. The standstill phase ends quickly as the at five specific phases (φ). The center of each panel corresponds material in the falling column is suddenly exhausted – the to the rest wavelength of the line (tick marks). The composite optical depth turns thin and to zero very quickly at wave- line profiles (black solid) are decomposed into red-shifted (red), lenths in the red lobe of the profile. blue-shifted (blue) optically thick components and the unshifted During the infall phase the velocity gradient can be ex- optically thin component (dotted green). The five vertical pan- pected to increase among the superficial, cooler layers, caus- els in the center illustrate (i) the relative positions (z: horizontal ing proportionally more heating there. Thus, the weakening lines) and (ii) motions (vectors) of six specific Lagrangian zones in of the C II doublet (first dip in Fig. 3) is consistent with a the atmospheres, (iii) the position relative to these layers where flattening of the gradient of the atmospheric temperature the monochromatic optical depth τ(λ) ≈ 1 (black dotted line), 3 and (iv) the location where each component of line absorption is and line source functions. Indeed, in the expectation of ac- likely to be strongest (shaded rectangles). Thus, for φ = 0.86, the companying increased turbulence, it seems difficult to un- optically thin stationary component (× shading) is formed below derstand how the weakening could arise in any other way. the optically thick red-shifted component ( / shading). These pro- The second dip of the C II curve features coinciding with the files should be compared with those in Fig. 7, and also with Fig. passage of the pulsation shock can be explained by a more 1 of Matthias et al. (1998). fundamental characteristic: the shock has a tendency to be more nearly isothermal than in the preshock atmosphere. The above picture is sketched qualitatively in Figure 9. because the effects of temperature increases are obvious for This illustration depicts the evolution of the stellar radius other lines but lead to a contradiction for the response of (top) and the absorption profiles (bottom) during five phases the C II features. Adding additional turbulence from a shock (φ), including one just prior to and one just following the would make the disagreement worse by forcing the predicted primary shock passage interval. These line shapes may be absorptions to be larger. compared to those in Fig. 7 or Fig. 1 of Mathias et al. (1998) and are additionally indicated as having blue-shifted, red-shifted and/or stationary components. The five central 4.4 Physical effect of the shocks on the He I and panels show a representation of several notional “layers”. CIV lines From left to right, these are shown to be falling inwards (ar- If enhancements of neither temperature nor turbulence can rows), and then arrested and reversed by material moving explain the line weakening, let us consider instead the ef- upwards from beneath. Compression gives rise to heating fect of a flattening of the temperature gradient with atmo- spheric depth, particularly in the construct of an LTE Milne- 3 Eddington atmosphere. In this formulation the strengths of A fact which may bear on this discussion is that to repro- duce UV spectrophotometic signatures from line aggregates in weak lines should simply be proportional to the gradient BW Vul’s IUE/SWP-camera spectra, Smith (2001) found it nec- dT/dτ. To interpret the enhanced absorptions in the blue essary to impose arbitrarily an artificial steepening of the tem- wings of the He I lines (and possibly C IV) at φ = 0.9, one perature gradient for a simulated model atmosphere at minimum should also consider the heating effects from infall of mate- light phase. This is equivalent to imposing a flattening of the gra- rial above where a line is being formed. At this phase, upper dient in the maximum light phase, as suggested from this optical strata are returning toward the surface at nearly free-fall study.

c 2002 RAS, MNRAS 000, 1–12 Shocks in the Atmosphere of BWVul 11 and a flattening of the temperature gradient. In turn this ing cannot be the whole story. Indeed, the realization that gives rise to absorption in optically thin layers (φ = 0.86), the C II doublet weakens during both shocks, and that the represented by a shaded rectangle (×). Other line compo- line strengths are insensitive to temperature variations, has nents are also represented, displaced according to whether all but forced the idea that the atmospheric temperature they are formed in outflowing (blue-shifted, solid), station- gradient is likely to be substantially flattened during shock ary (no shift, shaded × ) or infalling (red-shifted, shaded / passages. The heating of the atmosphere causes the column ) material. The zero velocity reference position or, equiva- length of excited atoms to increase, but at the same time it lently, the rest wavelength for the absorption line is marked causes the line source function gradient to decrease slowly at the bottom of each panel. On the basis of observations outwards, thereby producing line weakening of the saturated presented here, a broken line indicates where the atmosphere lines especially, such as the C II doublet. becomes optically thick across the line profile (τλ = 1). With this rough sketch in mind, we believe the time Whether absorption lines are formed in optically thick or is ripe for new investigations of BW Vul to undertake a thin layers is suggested by their proximity to this curve. In more quantitative analysis. This can begin with the aban- any case, while admitting the omission of critical details of donment of a static model atmosphere treatment, at least for transfer of photons across the profile as the line as it turns the phase intervals in which shocks affect the atmosphere’s optically thick, it appears possible that we can understand thermal and density structure. Another logical step is to the formation of the excess optically thin absorption in the construct “toy atmospheres” in which radiative and/or hy- blue wing of the He I lines as well as the weakening of the drostatic equilibrium are abandoned to see what devices temperature-sensitive C II and Si II lines. “work,” and to give some insight into the construction of Suffice it to say that in contrast to the infall shock the a new generation of hydrodynamic models of shocks. A line heating associated with the infall shock in our picture will synthesis from such kinematical atmospheres, in the spirit of extend over a broader range of strata in the atmosphere at Stamford & Watson’s early modeling, can point the way to any given moment than heating from the primary shock. a more correct treatment of line doubling/broadening and If the UVC and HeII and SiII line curves are to be taken strenth variations. One aspect especially worth investigating as diagnostics of atmospheric heating, the pulsation shock is the effect of desaturation in various lines. One needs to is more impulsive and liberates more heat per unit time know just how much pile-up material above the photosphere than the infall shock. In contrast, according to the equiva- is required to give each type of lines a blue lobe strength that lent width curves of Si II λ6371, the heating from the infall is some chosen fraction (say, one third) of the strength of the shock not only lasts longer, but by differing amounts from red lobe. In principle, combining these column densities with cycle to cycle. This suggests that the details of this heat- the observed rate of pile up at a given level will permit a ing are driven by the strength of the earlier pulsation wave. test of our hypothesis that the Van Hoof effect in this star’s Also, as noted in §3.2.3, the velocity jump criterion leads atmosphere is an artifact of the optical thinesses of the blue to the opposite inequality of apparent shock strengths, with lobes of these lines. the radial velocity jump to the standstill (infall shock) being In this paper the role of non-LTE has not been dis- typically larger than the jump at the end of the standstill cussed. However, transfer of photons through the line pro- (primary shock). Since the velocity and equivalent width file is ultimately essential to the testing of our ideas of how variations measure different types of shock properties, this the excess blue wing can develop in the He I lines during apparent disagreement of the inequalities need not be a con- the double-lobed infall-shock phase (φ = 0.9). The details tradiction to the model. of line transfer and amount of turbulence associated with the shocks are interrelated, and together they are critical to a description of these lines at these phases. Another as- pect of non-LTE formation processes concerns the behavior 5 CONCLUSIONS of the He I lines during the low-density (maximum radius) In this paper we have emphasized the importance of shock phase. The equivalent widths of the triplet λ5875 line give heating accompanying the passage of both shocks through no indication that metastability is important in the lower 3 the formation regions of several lines having a large range level (2 P) of this transition, as would be expected for low of excitation potentials (0–41 eV). We have also pointed out (supergiant-like) atmospheric densities. This fact certainly by contrast that density variations are likely to play at most means that the densities at this phase are not “too low,” but a minor role in the observed line strength changes. Several what this means quantitatively needs to be demonstrated. studies have remarked in the past on some of the optical An even more sensitive indicator of low densities is the He I and UV signatures we have discussed in detail, but the vari- λ10830 line. Because of the importance of stimulated emis- ations in the past were attributed to kinematical, density, sion for infrared transitions, this feature is well known to and/or finite propagation velocity effects – rarely heating. exhibit a strong response to either “excess” absorption or Even the Young et al. (1987) study did not pursue the sub- emission. ject beyond noting that variations of temperature-sensitive The heating of the base and rapid-acceleration regions lines. This general inattention to the subject was not made of the wind also remains to be evaluated. How hot these through an explicit error by any of these investigators. In regions can become, and thus how much pulsational energy fact, our own assessment of the importance of temperature is dissipated in the atmosphere, can be addressed by far-UV effects could not have come about except through echelle (FUSE satellite) observations of the O VI resonance doublet. observations over a broad wavelength range, particularly in- Finally, one wonders about the effects of shocks in cluding the red He I lines. Even so, the observation that the the outer atmospheres of other β Cep variables. Campos & He I lines show strength variations due to atmospheric heat- Smith (1981) and Smith (1983) examined high-resolution

c 2002 RAS, MNRAS 000, 1–12 12 M. A. Smith and C. S. Jeffery line profiles of several β Cep stars and found signatures of Liberman, M. A. & Velikovich, A. L. 1986, Physics of Shock Waves velocity jumps they associated with shocks in either opti- in Gases and Plasmas, (Berlin: Springer-Verlag). cal or UV lines of all five of the ones for which line profiles Massa, D. 1994, Ap. Space Sci., 221, 113 they examined. In an analysis of ν Eridani, Smith (1983) ar- Mathias, P., Gillet, D., Fokin, A. B., & Cambon, T. 1998 A. & gued that rapid changes during key phases in the velocity A., 339, 525 McCarthy, J. K., Sandiford, B. A., Boyd, D., & Booth, J. 1993, curve and optical Si III line profiles of this star suggest the Pub. ASP, 105, 881 presence of atmospheric shocks, though not necessarily dis- Odgers, G. J. 1955, Pub. Dom. Ap. Obs.,10, 215 continuities in a radial velocity curve. Indeed, the equivalent Owocki, S. P., & Cranmer, S. R. 2002, Radial and Nonradial width of the these lines grows probably due to the growth of Pulsations as Probes of Stellar Physics, ASP Conf., ed. C. a blue lobe. Unfortunately, other nonradial pulsation modes Aerts, T. Bedding, & J. Christensen-Dalsgaard, Vol. 259, 512 are likely to confuse the investigation of shock signatures.A Pigulski, A. 1993, A. & A., 274, 269 more promising candidate may be another large-amplitude Piskunov, N. E., & Valenti, J. A., 2002, A. & A., 385, 1095 variable, σ Scorpii. Campos & Smith (1980) have observed Smith, M. A. 1983, ApJ, 265, 338 red-wing emission in the Si III triplet lines of this star near Smith, M. A. 2001, ApJ, 562, 998 minimum velocity phase. Could the heating associated with Sterken, C. 1993, A. & A., 270, 259 Stamford, P. A., & Watson, R. D. 1978, Proc. Astron Soc. Aus- the pulsation shock in this star be occasionally so large as tralia, 3, 275 to produce emission? This star’s line profiles have appar- Stamford, P. A., & Watson, R. D. 1981, Proc. Astron Soc. Aus- ently not yet been extensively monitored since, but it might tralia, 4, 210 be profitable to search for the cause of emission and to see Van Hoof, A., & Struve, O. 1953, Pub. ASP, 65, 158 how this relates to the larger-amplitude shock of BW Vul for Young, A., Furenlid, I., & Snowden, M. S. 1981, ApJ, 245, 998 which no emissions are observed. (YFS)

ACKNOWLEDGMENTS We wish to express our thanks to the McDonald Telescope Allocation Committee for their granting of three nights of 2.1-meter telescope time. We are also grateful to Dr. Chris Johns-Krull for his reductions of the McDonald data to echellogram format. We thank Dr. Jeff Valenti for the loan of his interactive wavelength calibration program and Mr. Anthony Valenti for his time and instructions on the use of this program.

REFERENCES Aerts, C., Mathias, P., Van Hoolst, T., De Mey, K., Sterken, C., & Gillet, D. 1995, A. & A., 301, 781 Alvarez, R., Jorissen, A., Plez, B., Gillet, D., & Fokin, A. 2000, A. & A., 362, 655 Burger, M., de Jager, C., van den Oord, G. H., Sato, N. 1982a, A. & A., 107, 320 Burger, M., de Jager, C., van den Oord, G. H. 1982b, A. & A., 109, 289 Campos, A. J., & Smith, M. A. 1980, ApJ, 238, 550 Cohen, D. H. 2000, The Be Phenomenon in Early-Type Stars, ed. M. Smith, H. Henrichs, & J. Fabregat, ASP Conf. Ser., 214, 156 Crowe, R., & Gillet D. 1989, A. & A., 211, 365 Furenlid, I., Young, A., Meylan, T., Haag, C., & Crinklaw, G. 1987, ApJ, 319, 264 Goldberg, B. A., Walker, G. A. H., & Odgers, G. J. 1976, AJ, 81, 433 Garnier, D., Nardetto, N., Mathias, P., Gillet, D. & Fokin, A. B., Radial & Nonradial Pulsations as Probes of Stellar Physics, ed. C. Aerts, T. Bedding, & J. Christensen-Dalsgaard, 259, 206 Hinkle, K., Wallace, L., Valenti, J., & Harmer, D. 2000, Visible & near-IR Atlas of the Arcturus Spectrum, ASP, ... Horvath, A., Gherega, O., & Farkas, L. 1997, Rom. A. J., 8, 89 Hubeny, I., Lanz, T., & Jeffery, S. 1994, Newslett. Anal. Atron. Spectra, 20, 30 Kurucz, R.L. 1990, Trans. IAU, 20B, 169

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